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Mathematics
| Department Information |
Department of Mathematics and Computer Science
College of Science
Office: North Science 335
Phone: (510) 885-3414
| E-mail: mathcs@csueastbay.edu Website: http://www.sci.csueastbay.edu/mathcs | |||||
Phone: (510) 885-4011
| Professors Emeriti Edward L. Keller, Ph.D. University of Michigan Christopher L. Morgan, Ph.D. Brandeis University William R. Nico, Ph.D. University of California, Berkeley Bruce E. Trumbo, Ph.D. University of Chicago Professors Edward A. Billard, Ph.D. University of California, San Diego Kevin A. Brown, Ph.D. University of South Carolina Kevin E. Callahan (Chair), Ph.D. University of California, San Diego James S. Daley, Ph.D. University of California, Berkeley Julie S. Glass, Ph.D. University of California, Santa Cruz Kathleen Hann, Ph.D. University of California, Davis Gary E. Lippman, Ph.D. University of California, Riverside Michael K. Mahoney, Ph.D. University of California, Santa Barbara Massoud Malek, Ph.D. University of Houston Edna E. Reiter, Ph.D. University of Cincinnati Istvan Simon, Ph.D. Stanford University Stuart Smith, Ph.D. University of California, Berkeley William Thibault, Ph.D. Georgia Institute of Technology Donald L. Wolitzer, Ph.D. Northeastern University Ytha Y. Yu, Ph.D. University of California, Berkeley Associate Professors Jagdish Bansiya, Ph.D. University of Alabama, Huntsville Leann Christianson, Ph.D. University of South Carolina Levent Ertaul, Ph.D. University of Sussex (United Kingdom) Lynne L. Grewe, Ph.D. Purdue University Hilary J. Holz, D.Sc. George Washington University C. Matthew Johnson, Ph.D. College of William and Mary Dan Jurca, Ph.D. Northwestern University Chung-Hsing OuYang, Ph.D. University of California, Berkeley Farzan Roohparvar, Ph.D. Iowa State University David Yang, Ph.D. Columbia University Assistant Professors Roger W. Doering, Ph.D. University of California, Berkeley Madhavi D. Gandhi, Ph.D. University of California, Davis Julia Olkin, Ph.D. Rice University Ellen Veomett, Ph.D. University of Michigan Shirley Yap, Ph.D. University of Pennsylvania Lecturers Susan Benjamin, M.S. California State University, Hayward Jack A. Carter III, Ph.D. University of Texas Francis Conlan, Ph.D. University of California, Davis Michael A. Contino, M.A. Villanova University Dorothy E. Fujimura, M.S. University of Illinois Philip D. Gonsalves, B.S. California State University, Hayward Ching-Cheng Lee, Ph.D. University of London (England) Denise Sargent-Natour, M.A. Wayne State University Jean Simutis, Ph.D. University of California, Davis Vincent Slivinsky, Ph.D. The Pennsylvania State University | |||||
Please consult the 2010-2011 online catalog for any changes that may occur.
| Program Description |
Modern technological society has many fields that need specialists in mathematics. The Department of Mathematics and Computer Science offers a variety of courses intended for those who want to pursue a career in mathematics as well as those who wish to develop quantitative and problem-solving skills for use in other fields.
Students choose to major in mathematics for a number of reasons. Some intend to become high school, community college, or university teachers. Others seek careers in business, industry, or government, where mathematically trained people are in demand. An undergraduate major in mathematics is one of the best preparations not only for studying advanced Mathematics, but also for graduate work in Computer Science, Statistics, Operations Research, Actuarial Science, and the Natural Sciences. Most law schools are pleased to accept students with rigorous and logical training in Mathematics.
Many students combine their study of mathematics with the study of computer science. A popular option is to obtain a double major in Mathematics and Computer Science. Or students may earn a major in one of these fields and minor in the other.
The major requires six lower division courses and eleven upper division mathematics courses. The requirements are flexible enough that a student can choose one of several options according to his/her interest.
Each student is assigned a faculty advisor when (s)he declares a major and should consult this advisor regularly. A booklet containing a number of sample schedules, as well as further information about the mathematics major, is available in the Mathematics/Computer Science Student Service Center (North Science 337) or see the departmental website.
Although it is not a requirement, mathematics majors are urged to take as many courses as possible in an area such as Biology, Chemistry, Economics, Management Sciences, Physics, or Statistics. These are all fields where Mathematics plays a significant role, and it is important for a mathematics major to appreciate the relevance of the subject in applications. Study of one or more foreign languages is also recommended, especially for those students anticipating graduate study.
Student Learning Outcomes
Students graduating with a B.S. in Mathematics from Cal State East Bay will:
| 1. | possess technical competence including uses of calculus, linear systems, differential equations; understanding of axiomatic systems; abilities to read and create proofs; | ||||
| 2. | possess a fundamental understanding of Mathematics theory including: (a) applications of calculus, linear systems, (b) relations of algebraic systems and classical problems, and (c) roles of definitions and proofs in algebra and analysis; | ||||
| 3. | be able to work effectively as a team member; | ||||
| 4. | have an understanding of their professional and ethical responsibilities and appreciate the impact of mathematics in the societal context; | ||||
| 5. | communicate effectively, both in written and oral form. | ||||
| Career Opportunities |
Actuary • Computer Analyst • Cryptologist • Economist • Engineer • Engineering Analyst • Financial Analyst • Market Researcher • Mathematician • Numerical Analyst • Operations Research Analyst • Personnel Representative • Programmer • Professor/Teacher • Publisher Representative • Statistician • Stockbroker • Technical Writer
| Features |
Cal State East Bay students can participate in the Mathematics Club, which features lectures by students and faculty and offers a variety of social activities.
Each year the department awards a number of scholarships covering a portion of fees for the subsequent year. Scholarship applications may be obtained from the department student service center office during the Winter quarter.
Qualified upper division and graduate students may be employed as graders for classes. Also, students may earn credit in mathematics by tutoring in the Mathematics Lab.
Students who intend to earn a high school teaching credential after graduation may apply most of their mathematics major courses to meet the standards of California's Single Subject Matter Preparation Program for a Single Subject Credential in Mathematics.
Math majors who continue on to earn a master's degree in mathematics may pursue a career as a community college mathematics teacher.
| Preparation |
For Advanced Placement course equivalencies, see Registration chapter.
| Major Requirements (B.S.) |
Because requirements are subject to change, consult an advisor in your major department for clarification and interpretation of your major requirements. The major consists of 72 units; the BS degree requires a total of 180 units.
| I. | Lower Division Requirements (28 units) | ||||
| This requirement consists of the following seven courses: | |||||
| MATH 1304, 1305, 2304, 2305 The Calculus sequence CS 1160 Introduction to Computer Science and Programming Methods MATH 2101 Elements of Linear Algebra MATH 2150 Discrete Structures | |||||
| (Mathematics majors may substitute MATH 3151 or MATH 4151 for MATH 2150.) | |||||
| A student who has recently taken a pre-calculus course in high school should be prepared to begin the calculus sequence. A student with three years of high school mathematics, including two years of algebra and one year of geometry, should be prepared to take MATH 1130, or possibly MATH 1300. Students who are unsure about what mathematics course to begin with should call the department office. Students may not enroll in any baccalaureate level mathematics or computer science courses unless they have met the Entry Level Mathematics (ELM) requirement, or are exempt from it. Contact the Testing Office 885-3661 for more information. | |||||
| II. | Upper Division Requirements (44 units) | ||||
| Every Mathematics major is required to complete one of the following options: Option A (44 units) | |||||
| Required courses: | |||||
| MATH 3000 Introduction to Abstract Mathematics and Proofs (4) (Mathematics majors are encouraged to take MATH 3000 as early as possible.) MATH 3100 Linear Algebra (4) MATH 3331 Differential Equations (4) | |||||
| The following two sequences: | |||||
| MATH 3121-3122 Abstract Algebra I and II (4, 4) MATH 3300-3301 Analysis I and II (4, 4) | |||||
| One sequence from the following five: | |||||
| MATH 3151-4151 Combinatorial Mathematics (4, 4) MATH 3215-4215 Geometry (4, 4) MATH 3361-4361 Differential Equations (4, 4) MATH 3750-4750 Numerical Analysis (4, 4) MATH 3841-4841 Optimization (4, 4) | |||||
| Electives: Two upper division mathematics courses (8 units), which may include any cross-listed, upper division course in Statistics or Computer Science (but not MATH 4012, 4013, 4014). | |||||
| Option B - Applied Mathematics (44 units) | |||||
| Required courses: | |||||
| MATH 3000 Introduction to Abstract Mathematics and Proofs (4) (Mathematics majors are encouraged to take MATH 3000 as early as possible.) MATH 3100 Linear Algebra (4) MATH 3331 Differential Equations (4) | |||||
| Three out of the four courses from the following two sequences: | |||||
| MATH 3121-3122 Abstract Algebra I and II (4, 4) MATH 3300-3301 Analysis I and II (4, 4) | |||||
| Two sequences from the following four: | |||||
| MATH 3151-4151 Combinatorial Mathematics (4, 4) MATH 3361-4361 Differential Equations (4, 4) MATH 3750-4750 Numerical Analysis (4, 4) MATH 3841-4841 Optimization (4, 4) | |||||
| Electives: One upper division mathematics course (4 units), which may include any cross-listed, upper division course in Statistics or Computer Science (but not MATH 4012, 4013, 4014). | |||||
| Option C - Mathematics Teaching (44 units) | |||||
| Required courses: | |||||
| MATH 3000 Introduction to Abstract Mathematics and Proofs (4) (Mathematics majors are encouraged to take MATH 3000 as early as possible.) | |||||
| MATH 3121 Abstract Algebra I (4) MATH 3100 Linear Algebra (4) MATH 3215 Geometry I (4) MATH 3300 Analysis I (4) MATH 3331 Differential Equations (4) MATH 3600 Number Theory (4) MATH 4040 History of Mathematics (4) STAT 3401 Introduction to Probability Theory I (4) | |||||
| One from the following three courses: | |||||
| MATH 3122 Abstract Algebra II (4) MATH 3301 Analysis II (4) MATH 4215 Topics in Geometry (4) | |||||
| Electives: One upper division mathematics course (4 units), which may include any cross-listed, upper division course in Statistics or Computer Science (but not MATH 4012, 4013, 4014). A student who completes Option C can satisfy rather easily the requirements for the State-approved Single Subject Matter Preparation Program in Mathematics, a program of courses designed to prepare the student for entry into the Credential Program in Mathematics, provided that judicious choices of mathematics elective courses and general education courses are made. To accomplish this, the student who completes Option C must: | |||||
| 1. | choose MATH 4901 Senior Seminar (4) in the mathematics elective category; | ||||
| 2. | complete STAT 3502 Statistical Inference (4); and | ||||
| 3. | complete TED 3001 Exploring Education (3) and/or other field experience approved by the Mathematics Subject Matter Preparation Adviser: at least 45 hours of classroom experience in an instructional capacity is required. | ||||
| Other Degree Requirements |
In addition to major requirements, every student must also complete the University requirements for graduation which are described in the Baccalaureate Degree Requirements chapter in the front of this catalog. These include the General Education-Breadth requirements; the second composition (ENGL 1002) requirement; the cultural groups/women requirement; the performing arts/activities requirement; the U.S. history, U.S. Constitution, and California state and local government requirement; the University Writing Skills Requirement; and the residence, unit, and grade point average requirements.
| Minor Requirements |
| The minor consists of 28 units. | |||||
| Required courses: | |||||
| MATH 1304 Calculus I (4) MATH 1305 Calculus II (4) MATH 2101 Elements of Linear Algebra (4) MATH 2304 Calculus III (4) | |||||
| Two courses from the following list: | |||||
| MATH 3100 Linear Algebra (4) MATH 3121 Abstract Algebra I (4) MATH 3215 Geometry I (4) MATH 3300 Analysis I (4) MATH 3331 Differential Equations (4) | |||||
| One 4-unit upper division mathematics course, which may include any cross-listed, upper division course in Statistics or Computer Science (but not MATH 4012, 4013, 4014). | |||||
| Minor in Computer Science |
| The complete description of this minor may be found in the undergraduate Computer Science section of the current Cal State East Bay catalog. It is relatively easy for a Mathematics major to complete a minor in Computer Science. To do this, the student should take the following courses in addition to those required for the mathematics major. | |||||
| CS 2360 Programming Methodology and Introduction to Software Engineering (4) CS 2430 Computer Organization and Assembly Language Programming (4) | |||||
| Three upper division courses as follows: | |||||
| A. | Two courses from the following list: | ||||
| CS 3120 Programming Language Concepts (4) CS 3240 Data Structures and Algorithms (4) CS 3430 Computer Architecture (4) CS 4560 Operating Systems (4) | |||||
| B. | One upper division Computer Science elective. This may be a third course from (A) or any course from category IV of the requirements for the major in Computer Science. | ||||
| Single Subject Matter Preparation Program |
See the Single Subject Matter Preparation Program chapter in the undergraduate section of this catalog for a description of the Single Subject Matter Preparation Program in Mathematics.
| Certificate in Foundational Mathematics Teaching |
The certificate consists of 21 units.
Required Courses (21 units):
| MATH 1130 College Algebra (4) MATH 4012 Geometry and Measurement (4) MATH 4013 Statistics, Data Analysis, and Probability (4) MATH 4030 Advanced Study of School Mathematics (4) TED 5390 Instructional Methods for the Single Subject Classroom I (3) TED 5391 Instructional Methods for the Single subject Classroom II (2) | |||||
| Basic Skills Courses |
| The course prefix for the following courses is MATH. | |
| 0801, 0802  | Elementary Algebra A and B (4 each) A two-quarter sequence in basic mathematics and elementary algebra. On successful completion of this sequence, students should register for MATH 0950. Prerequisites: MATH 0801- appropriate ELM score (ranges available from the Testing Office or at http://www.csueastbay.edu/ge/remedialinfo/scores.htm); MATH 0802 - Grade of CR in MATH 0801. Not for credit toward baccalaureate degree. CR/NC grading only. |
| 0899 | Elementary and Intermediate Algebra Self-Paced (4) Topics from basic mathematics, elementary and intermediate algebra. Self-paced, offered Summer only. Variable required on-campus hours to be arranged. Students will re-take the ELM for placement at the end of the course. Units will not count toward the baccalaureate degree. Prerequisite: Entering Freshman status; appropriate ELM score (ranges available from the Testing Office or at http://www.csueastbay.edu/ge/remedialinfo/scores.htm). CR/NC grading only. |
| 0900 | Elementary Algebra (4) A one quarter course in elementary algebra. On successful completion of this course, students should register for MATH 0950. Prerequisite: appropriate ELM score (ranges available from the Testing Office or at http://www.csueastbay.edu/ge/remedialinfo/scores.htm). Not open to students with credit for MATH 0802. Not for credit toward baccalaureate degree. CR/NC grading only. |
| 0911 | Algebra Lab (2) Supplemental study, discussion, and practice in the theory, problems, and applications of elementary and intermediate algebra. Co-requisite: enrollment in MATH 0801, 0802, 0900, or 0950. Not for credit toward baccalaureate degree. May be repeated once for credit (non-baccalaureate), with permission of the Math/CS Department, for a maximum of 4 units. CR/NC grading only. |
| 0950 | Intermediate Algebra (4) Operations with algebraic expressions, exponents and radicals; linear and quadratic equations; systems of equations and inequalities; linear and quadratic functions and their graphs; elementary conic sections; word problems. Prerequisite: Grade of CR in MATH 0802 or MATH 0900; or an appropriate ELM score (ranges available from the Testing Office or at http://www.csueastbay.edu/ge/remedialinfo/scores.htm). Not for credit toward baccalaureate degree. CR/NC grading only. |
| Undergraduate Courses |
The course prefix for the following courses is MATH.
Computer Science courses offered by the Department of Mathematics and Computer Science are fully described in the Computer Science section of this catalog.
A student who has recently taken a pre-calculus course in high school should be prepared to enter calculus. A student with three years of high school mathematics, including two years of algebra and one year of geometry, should be prepared to take MATH 1130, or possibly MATH 1300. Such students, and others who are unsure about what mathematics course to begin with, should call the Mathematics and Computer Science Department for advice. Also, Assessment and Testing (885-3661) offers placement tests that can assist students in finding the appropriate starting class.
1110 | The Nature of Mathematics (4) This course is designed to introduce the student to mathematics as an art and mathematics as a tool, emphasizing the place of mathematics in today's world. Will satisfy the general education requirement for nonmajors. Prerequisite: satisfactory completion of Entry-Level Mathematics requirement. |
| 1130 | College Algebra (4) Functions and graphs: polynomials, rational functions, exponential and logarithmic functions. See note at beginning of course listings. Prerequisite: satisfactory completion of Entry-Level Mathematics requirement. |
| 1300 | Trigonometry and Analytic Geometry (4) Definitions, properties and graphs of the trigonometric functions. Applications. Analytic geometry of conic sections. A preparatory course for calculus. See note at beginning of course listings. Prerequisites: MATH 1130 or departmental permission. |
| 1304 | Calculus I (4) Differential calculus. Limits and continuity. Exponential and logarithmic functions. Techniques and applications of differentiation. See note at beginning of course listings. Prerequisite: MATH 1300 or departmental permission. |
| 1305 | Calculus II (4) Integral calculus. The indefinite integral, area, the Fundamental Theorem and techniques of integration. Applications to volume, arc length, physical and biological problems. Prerequisite: MATH 1304. |
| 1810 | Mathematics for Business and Social Sciences I (4) Functions and graphs; exponential and logarithmic functions; mathematics of accounting and finance; matrices and systems of equations; geometric approach to linear programming; introduction to differential and integral calculus with applications to business and social sciences. Prerequisite: MATH 1130. |
| 1820 | Mathematics for Business and Social Sciences II (4) Further topics in derivatives and integration, elementary differential equations; multivariable calculus, Lagrange multipliers, systems of linear equations, matrix algebra; inequalities and linear programming; applications to business and social sciences. Prerequisites: MATH 1810. |
2011 | Number Systems (4) Structure of number systems, place value, whole numbers, integers, fractions, decimals, real numbers. Standard and nonstandard algorithms, mental computation. Algebra as generalized arithmetic. Divisibility, prime and composite numbers, GCF, LCM. Ratio, proportion, percents. Prerequisite: satisfactory completion of the Entry Level Mathematics (ELM) requirement. Not open to students with credit for MATH 4021. |
| 2101 | Elements of Linear Algebra (4) Vector spaces, linear transformations, matrices, systems of linear equations. Stress on 2 and 3 dimensions, including geometric and other applications. Prerequisite: MATH 1305 or 1820 (may be taken simultaneously with, or after, MATH 2304). |
| 2150 | Discrete Structures (4) Topics in discrete mathematics. Elementary logic, set theory, and relations; induction, enumeration techniques, recurrence relations, trees and graphs. Boolean algebra, algorithm analysis. Prerequisite: MATH 1304. |
| 2304 | Calculus III (4) Infinite series, convergence of power series. Vectors in space. Partial derivatives, chain rule, directional derivative and gradient. Curves and surfaces. Maxima and minima. Multiple integrals. Prerequisite: MATH 1305. |
| 3000 | Introduction to Abstract Mathematics and Proofs (4) Introduction to methods and proof techniques in several branches of mathematics, with topics chosen from logic, set theory, abstract algebra, number theory, analysis, and graph theory. Provides a transition from lower division mathematics courses, which concentrate on computation, to upper division proof-oriented mathematics courses. Prerequisite: MATH 2304; co-requisite: MATH 2101. |
| 3100 | Linear Algebra (4) Abstract vector spaces, linear transformations, matrices and determinants. Dual spaces and inner product spaces. Eigenvalues and eigenvectors. Prerequisites: MATH 2101 and either 2150 or 3000. (MATH 3000 is strongly encouraged for mathematics majors and may be taken concurrently with MATH 3100.) |
| 3121 | Abstract Algebra I (4) Equivalence relations, binary operations. Integers: divisibility, factorization, integers modulo n. Groups: subgroups, cyclic groups, permutation groups, quotient groups. Homomorphisms and isomorphisms. Selected topics as time permits. Prerequisites: MATH 2101and either 2150 or 3000. (MATH 3000 is strongly encouraged for mathematics majors and may be taken concurrently with MATH 3121.) |
| 3122 | Abstract Algebra II (4) Rings and fields: integral domains, ideals, quotient rings, polynomial rings, roots of polynomials, algebraic extensions and finite fields. Selected topics as time permits. Prerequisite: MATH 3121. |
| 3151 | Combinatorics (4) Theory of counting, including partitions, Stirling numbers, generating functions. Applications of Burnside's lemma from multiple transitivity to the Polya-Redfield Theorem. Ferrers diagrams, symmetric functions, and majorization. Prerequisites: MATH 2101 and either 2150 or 3000. |
| 3215 | Geometry I (4) An axiomatic approach to incidence, neutral, Euclidean, and non-Euclidean plane geometry. Various models, such as the Euclidean, hyperbolic, and taxicab planes, will be considered throughout the course. Prerequisite: MATH 2101 and either 2150 or 3000. (MATH 3000 is strongly encouraged for mathematics majors and may be taken concurrently with MATH 3215.) |
| 3300, 3301 | Analysis I, II (4 each) The real numbers, limits, sequences and series of real numbers, Bolzano-Weierstrass theorem. Continuity, intermediate and extreme value theorems, uniform continuity, sequences of functions. Topology of Rn. Differentiation, chain rule, implicit and inverse function theorems. Prerequisites for MATH 3300: MATH 2101, 2304, and either 2150 or 3000. Prerequisite for MATH 3301: MATH 3300. (MATH 3000 is strongly encouraged for mathematics majors and may be taken concurrently with MATH 3300.) |
| 3320 | Calculus of Vector Functions (4) Differentiation and integration of vector valued functions; gradient, divergence, and curl; cylindrical and spherical coordinates; theorems of Green and Stokes. Prerequisite: MATH 2304 and MATH 2101 (2101 may be taken concurrently). |
| 3331 | Differential Equations (4) Methods of solution and applications of first order differential equations. Linear n-th order equations with emphasis on equations of 2nd order. Other topics may include power series solutions, Laplace transforms, linear systems. Prerequisite: MATH 2304. |
| 3361 | Ordinary Differential Equations (4) Series solution of linear differential equations with variable coefficients, two point boundary value problems, systems of differential equations, phase plane analysis. Prerequisites: MATH 2101 and 3331. |
| 3401, 3402 | Introduction to Probability Theory I, II (4 each) (See STAT 3401, 3402 for course descriptions.) |
| 3502, 3503 | Statistical Inference I, II (4 each) (See STAT 3502, 3503, for course descriptions.) |
| 3600 | Number Theory (4) Euclid's algorithm, prime numbers, congruences, theorems of Fermat and Euler, quadratic residues. Prerequisites: MATH 2101 and either 2150 or 3000. (MATH 3000 is strongly encouraged for mathematics majors and may be taken concurrently with MATH 3600.) |
| 3750 | Numerical Analysis I (4) Basic numerical methods and analysis; practical solutions of problems from engineering, science, and mathematics. Computer representation of real numbers, errors, root finding, interpolation, numerical integration, ordinary differential equations. Prerequisites: CS 1160, MATH 2101 and 2304. Cross-listed with CS 3750. |
| 3841 | Linear Programming (4) Problems of maximizing or minimizing a linear function subject to linear constraints; typical applications involve planning ("programming") the allocation of limited resources to achieve an optimal result. Topics include problem formulation, solution procedures, duality theory, sensitivity analysis, special problems (e.g., transportation and assignment problems). Prerequisite: MATH 2304 and competence in matrix algebra. |
| 3875 | Mathematical Physics (4) Mathematics theory and methods with applications to physics. In class physics laboratory explorations will utilize mathematical techniques to better understand physics phenomena. Prerequisite: MATH 1305. Co-requisite: MATH 2304. Cross-listed with PHYS 3875. |
| 3898 | Cooperative Education (1-4) Supervised work experience in which student completes academic assignments integrated with off-campus paid or volunteer activities. Prerequisites: at least 2.0 GPA; departmental approval of activity; completion of lower division Mathematics major requirements and upper division standing. A maximum of 2 units will be accepted toward the Mathematics major. May be repeated for credit, for a maximum of 8 units. CR/NC grading only. |
| 4012 | Geometry and Measurement (4) Properties of 2- and 3-dimensional figures including congruence, similarity, proportional reasoning, area, perimeter, volume, surface area. Informal constructive proofs of properties of angles, polygons, parallel lines and Pythagorean theorem. Transformational geometry. Measurement systems, estimation, coordinate geometry. Prerequisite: MATH 2011. Not open to students with credit for MATH 4022. |
| 4013 | Statistics, Data Analysis, and Probability (4) Displaying and interpreting data via graphs, tables and charts. Descriptive statistics, including mean, median, mode and range. Basic Survey design, including possible sources of biases. Elementary discrete probability. Dependent and independent events. Prerequisites: MATH 2011 and satisfactory completion of the Entry Level Mathematics requirement. Cross-listed with STAT 4013. Not open to students with credit for MATH 4023. |
| 4014 | Algebra and Functions (4) Patterns and functional relationships. Linear and quadratic equations and inequalities. Interpretation of graphs, multiple representations of functions. Factoring and completing the square. Proportional reasoning. Systems of linear equations. Prerequisites: MATH 2011 and satisfactory completion of the Entry Level Mathematics requirement. Not open to students with credit for MATH 4024. |
| 4030 | Advanced Study of School Mathematics (4) Foundations of school mathematics from an advanced standpoint. An in depth study of middle and high school level algebra, geometry and number theory and its applications, theoretical foundations and extensions. Intended for prospective elementary and middle school teachers. Prerequisites: Math 2011 and Math 1130 or consent of instructor. Not for credit in Mathematics or Computer Science major. A-F grading only. |
| 4040 | History of Mathematics (4) The historical development of mathematical ideas and techniques. Prerequisite: calculus or consent of instructor. |
| 4100 | Mathematical Logic (4) The propositional calculus and its completeness. Boolean algebras. Functional calculi of various orders. Theorems of Godel and Henkin. Prerequisite: Senior standing in mathematics or consent of instructor. |
| 4121 | Advanced Algebra (4) Theory of groups, including factor groups, Jordan-Holder Theorem, Sylow theorems. Mappings and homomorphisms. Introduction to rings and fields. Topics continued in MATH 6121. Prerequisite: MATH 3122. |
| 4151 | Graph Theory (4) Introduction to graph theory. Graphic sequences. Planar graphs and the theorems of Euler and Kuratowski. Bipartite graphs. Connectivity and spanning trees. Hamiltonian graphs. Matching, chromatic and characteristic polynomials. Cospectral graphs and the graph isomorphism problem. Algorithms. Prerequisites: MATH 2101 and either 2150 or 3000. |
| 4170 | Theory of Automata (4) (See CS 4170 for course description.) |
| 4215 | Topics in Geometry (4) Topics in geometry such as algebraic, differential, finite, or projective geometry, convexity, packing and tiling, polytopes, and isoperimetric problems. Prerequisites: MATH 3215 or consent of instructor. May be repeated once for credit with consent of the chair, for a maximum of 8 units. |
| 4235 | Introduction to Knot Theory (4) An introduction to the theory of knots and links. Topics covered include Reidemeister moves, knot invariants, including 3-colorings, the linking number, the Alexander polynomial, the Kauffman bracket and Jones polynomial. As time permits, some applications in biology and/or chemistry will be discussed. Prerequisite: MATH 3121. |
| 4245 | Analysis of Algorithms (4) (See CS 4245 for course description.) |
| 4250 | Digital Geometry and Topology (4) Introduction to modern differential geometry and topology. Geometry of curves and surfaces, differential forms and vector fields, manifolds, curvature, geodesics, topological invariants. Prerequisites: Math 3100, 3300, or consent of instructor. |
| 4340 | Introduction to Complex Variables (4) Introduction to theory of functions of complex variables. Prerequisite: MATH 3300. |
| 4350 | Theory of Functions of a Real Variable (4) Pointwise and uniform covergence, Taylor series, Riemann integration, sets of measure zero, Lebesgue's theorem on the Riemann integral, the metric space of continuous functions, and selected topics. Prerequisite: MATH 3300. |
| 4360 | Introduction to Topology (4) Topological spaces, metric spaces, continuity, connectedness and compactness. Prerequisite: MATH 3300. |
| 4361 | Partial Differential Equations (4) Differential equations of physics: the wave equation, the heat equation, Laplace's equation; boundary-value problems. Elementary Sturm-Liouville theory, Fourier series, Fourier and Laplace transforms, Bessel functions, selected topics. Prerequisite: MATH 3331. |
| 4365 | Dynamical Systems (4) Introduction to dynamical systems and applications. Variational calculus, Lagrangian dynamics, principle of critical action, Hamiltonian systems and symplectic mechanics, Hamilton-Jacobi equation, chaotic and nonlinear systems, fractals. Prerequisites: MATH 3100, 3300, 3331, or consent of instructor. |
| 4401 | Introduction to Stochastic Processes (4) (See STAT 4401 for course description.) |
| 4412 | Probability Theory (4) (See STAT 4412 for course description.) |
| 4750 | Numerical Analysis II (4) Continuation of MATH 3750. Numerical solution of linear systems, matrix norms, approximation of functions, algebraic eigenvalues. Prerequisite: MATH/CS 3750. Cross-listed with CS 4750. |
| 4841 | Topics in Optimization (4) Sequel to MATH 3841. Topics to be drawn from linear and/or nonlinear programming. Linear programming topics may include integer programming, game theory, network programming; nonlinear programming topics include optimality conditions and solution procedures for unconstrained and constrained optimization problems. Prerequisite: MATH 3841. May be repeated once for credit with consent of the chair, for a maximum of 8 units. |
| 4845 | Fuzzy Sets and Fuzzy Logic (4) (See CS 4845 for course description.) |
| 4850 | Variational Calculus (4) Function spaces, general variation of a functional, Euler-Lagrange equations, Noether's theorem and conservation laws, Hamilton-Jacobi theory, canonical transformations and symplectic geometry. Prerequisites: MATH 3100 and MATH 3331. |
| 4900 | Independent Study (1-5) May be repeated for credit with consent of instructor, for a maximum of 12 units. |
| 4901 | Senior Seminar (4) Exploration of topics in mathematics. Topics selected from the literature to illustrate relationships among various areas of mathematics. Oral presentations and paper required. Prerequisite: senior standing in mathematics (completion of 32 units of mathematics courses) or permission of the instructor. |
| Footnotes |
| | Completion of MATH 0801-2 or MATH 0900 does not satisfy the ELM requirement. Students must also pass MATH 0950 before enrolling in a baccalaureate-level mathematics course. | |
| | Upper division mathematics and computer science majors will not receive credit for this course. | |
| | Intended for prospective elementary and junior high school teachers; Mathematics and Computer Science majors will not receive credit for this course. | |
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© 2009 The California State University
Last Updated: October 26, 2009